The former Liverpool striker scored his first goal in over two years, as the Blades leapfrogged Leeds United back to the top of the table.
Japhet Tanganga and George Saville both struck the woodwork for Millwall in what was Neil Harris' final home game in charge, but Brewster broke the deadlock just before the break.
Chris Wilder's side had to remain concentrated during the second half as the hosts pushed for the equaliser, but they held out for a crucial three points.
Elsewhere, Ruben Selles was unfortunate not to begin his tenure with bottom side Hull City in victorious fashion against Watford.
Chris Bedia broke the deadlock for the hosts in the 82nd minute, and it looked like it could be enough to give them their first win since early October.
However, Rocco Vata equalised for the visitors two minutes from time to prevent the Tigers from moving off the foot of the table and out of the relegation zone.
Meanwhile, West Bromwich Albion moved back into the top six as goals from Alex Mowatt and Karlan Grant secured a 2-0 win over Frank Lampard's Coventry City.
Queens Park Rangers and Preston North End both pulled clear of the relegation zone following 2-0 victories over Oxford United and Cardiff City respectively, and the Bluebirds remain in the bottom three due to their inferior goal difference.
The decisive moment came in the 52nd minute when Millwall captain Jake Cooper powerfully headed Femi Azeez's cross beyond the grasp of James Trafford.
But the Lions, who moved up to seventh in the table with the win, were worthy winners at The Den.
They registered 12 shots compared to Burnley's eight, ending with an expected goals (xG) total of 0.83 compared to their opponents' 0.17.
Parker's side managed just one effort on target, which came in the fourth minute courtesy of Luca Koleosho, with the Clarets boss lamenting his side's display in the final third.
"We came here knowing it's a tough place to come and dominated the first 25 minutes but the game went away from us at the back end of that first-half," Parker said.
"Emotionally, with a young team like ours we struggled in the big moments.
"We need to be more progressive in the front third but it's a really young team, a brand new team and we need to keep working hard.
"We lacked spark in the second-half and the game has been decided on a set play."
But for Millwall boss Neil Harris, he masterminded the Lions' first league triumph over Burnley since a 3-1 victory back in February 2012.
It was also a third consecutive 1-0 win for Millwall. Since the start of last season, they’ve won 13 Championship games by that scoreline, at least five more than any other side.
And Harris believes his side warranted their victory, insisting that his tactical decisions made the Clarets run out of ideas.
"It was a strong result and I thought Burnley ran out of ideas," Harris said.
"We grew into the game after Burnley were slightly better in the first 20 minutes, but I couldn't see them scoring against us.
"You just need a moment here at The Den and Jake Cooper produces it and, if anything, I thought we'd get the second goal.
"If we win games 1-0 it's fine and the first goal in the Championship is so important, especially for us."
Daniel Farke’s side came into Saturday's encounter having won back-to-back matches against Sheffield Wednesday and Hull City, but their momentum was halted by their clinical visitors.
Burnley forward Luca Koleosho scored the only goal of the game the day before his 20th birthday.
Koleosho took advantage of a slip from Manor Solomon after 18 minutes, before sprinting 70 yards and drilling a shot past Leeds goalkeeper Ilan Meslier.
That proved to be enough to inflict on Leeds a third home league defeat in six matches going back to last season, despite the hosts applying plenty of pressure as they sought an equaliser.
Burnley's Bashir Humphreys was sent off eight minutes into stoppage time at the end of the match, but Leeds were unable to find a way through.
Elsewhere in Saturday's early Championship kick-offs, Luton Town claimed their first win since relegation from the Premier League.
Teden Mengi's fine early effort from the edge of the penalty area was enough to beat Millwall 1-0 away from home.
While Luton have ground to make up in the promotion race, Oxford United's surprise challenge continues on the back of their 100% home record.
That was maintained with a deserved 1-0 victory over Stoke City, with Idris El Mizouni netting the winner three minutes into the second half.
Joe Rodon and Max Wober scored their first goals for Leeds as Daniel Farke's side bounced back from a 1-0 defeat to Blackburn Rovers in their last match.
While the Rams, who have only won once in their last 10 games, dropped to 16th place, Leeds overtook Sheffield United – who face West Bromwich Albion on Sunday – on goal difference.
Frank Lampard earned his first win as Coventry City boss as they beat hosts Millwall 1-0, ending a five-match winless run.
The former England and Chelsea midfielder took charge at Coventry last month, succeeding long-serving boss Mark Robins and his first win came courtesy of an Ephron Mason-Clark goal, which snapped Millwall's nine-match unbeaten run.
Tom Watson scored twice as Sunderland ended their six-match run without a win by defeating Stoke City 2-1 at the Stadium of Light.
The 18-year-old equalised for the hosts in the seventh minute, only a minute after Lewis Koumas put the Potter ahead, before he found the winner with a deflected strike three minutes from full-time.
Fourth-placed Sunderland are now only two points behind the top two.
Elsewhere in the Championship, a Sean McLoughlin own goal proved to be the difference between the sides as Blackburn edged Hull City 1-0.
New Hull manager Ruben Selles watched from the stands as his side fell to the bottom of the table while Rovers kept pace with the top four as they trail Sunderland by four points.
Yet the top two in England's second tier look increasingly likely to be the pair promoted to the Premier League, with third-placed Fulham suffering a damaging home defeat against Brentford.
In the first matches following the league's three-month coronavirus suspension, a new hero emerged for mid-table Derby County as 18-year-old Louie Sibley scored a hat-trick in their win at Millwall.
And Rhian Brewster, a striker on loan from Liverpool, gave Swansea City's play-off hopes a boost by netting twice at Middlesbrough, as well as making a powerful political statement.
POINT A MIXED BLESSING FOR BAGGIES
With Leeds in action at Cardiff City on Sunday, West Brom had an opportunity to go two points clear of Marcelo Bielsa's team as the league resumed.
Bilic's players dominated the derby clash and had a host of chances but could not find a breakthrough, and a stalemate at the Hawthorns potentially plays into the hands of Leeds.
The top two are now level on points, with West Brom top on goal difference, but Leeds will have the chance to go three clear before the next round of games.
BEES STING NEIGHBOURS
Said Benrahma and Emiliano Marcondes scored late for Brentford in a 2-0 win at promotion rivals Fulham, a result that leaves West Brom and Leeds seven points clear with eight games remaining for the play-off pack.
Nottingham Forest were heading for victory at Sheffield Wednesday after Joe Lolley gave the visitors a 69th-minute lead, only for Connor Wickham to grab a stoppage-time leveller for the Owls.
Forest sit fifth, four points clear of a Preston North End side who were held 1-1 at Luton Town, Callum McManaman firing a late equaliser for the hosts, who nevertheless fell to the foot of the table.
KING LOUIE
Blackburn Rovers beat Bristol City 3-1 in a battle between teams fighting with Preston for sixth place, but the individual performance of the day came from Sibley, whose heroics guided Derby to their 3-2 win at Millwall.
"I'm absolutely buzzing," Sibley told Rams TV. "To get that hat-trick was just unbelievable. When the third goal went in, I couldn't stop smiling."
Brewster was not far behind, his double steering Swansea to a 3-0 victory at lowly Middlesbrough.
Brewster held up a shirt that read "our colour is not a crime" after his first goal, expressing support for the Black Lives Matter movement.
TIGERS ON THE SLIDE
Wigan Athletic were 2-0 winners at fellow strugglers Huddersfield Town, while Hull City slipped into the bottom three after losing 1-0 at home against Charlton Athletic.
Barnsley climbed off the bottom by winning 1-0 at QPR, and Stoke City drew 1-1 at Reading.
Daniel Farke's Whites required a response to move back into the automatic promotion places after a win for Sheffield United on Tuesday, but instead they were beaten 1-0 by surprise package Millwall.
A fourth straight 1-0 win for the Lions was secured with a first-half Japhet Tanganga goal and moved them up to fifth, now just four points behind Leeds in third.
Leeds are themselves four points behind front-runners Sunderland, but that gap could have been wider had the Black Cats beaten Preston North End.
Just as at Queens Park Rangers on Saturday, though, Sunderland were held to a goalless draw away from home.
Jobe Bellingham was sent off against QPR and so missed out through suspension, and further bold changes from coach Regis Le Bris could have opened the door for Preston to snatch an unlikely win.
Instead, Preston remain among a clutch of teams just above the relegation zone, also including Luton Town and Cardiff City.
Luton beat Cardiff 1-0 with a Jacob Brown goal, while Coventry City lost 2-1 at home to Derby County. Stoke City were 2-0 winners at Blackburn Rovers.
Daniel Farke's side edged a seven-goal thriller with a last-gasp winner against Swansea City on Sunday, but had no such drama to contend with three days later at Elland Road.
Sam Byram scuffed an early chance but inadvertently teed up his own sumptuous volley for a 10th-minute lead, before Joel Piroe scored on the rebound from close range on the stroke of half-time.
Substitute Dan James made sure of a routine win in the second half as Leeds moved ahead of second-placed Sheffield United on goal difference, with that pair two points clear of Burnley.
At the other end of the table, Queens Park Rangers climbed off the bottom spot with a 2-0 away triumph over Cardiff City thanks to Zan Celar's first two goals for the club.
The Slovenia international faced heavy criticism after missing a penalty in Saturday's draw with Stoke City, but silenced his critics with strikes in either half at the Cardiff City Stadium.
Fellow strugglers Portsmouth slipped down to the bottom of the league after their match was postponed against Millwall due to floodlight failure at Fratton Park.
Play-off hopefuls Middlesbrough had scored 15 goals across their three-game winning streak, though that came to an abrupt halt after Dominic Hyam's 83rd-minute strike snatched victory for Blackburn Rovers.
Michael Carrick's side still sit sixth, occupying the last play-off spot, but Blackburn's victory saw them jump up to eighth and just two points behind their hosts at the Riverside.
Swansea City secured a 2-1 victory over Derby County in Wednesday's other game, with the visitors doing the damage in the first half after goals from Zan Vipotnik and Ronald.
Nathaniel Mendez-Laing pulled one back for Paul Warne's hosts at Pride Park, where defeat left Derby 15th and four places behind Swansea, who bounced back from successive defeats previously.
Delano Burgzorg netted his first two Championship goals for Boro, opening the scoring with a well-worked corner in the 30th minute before Emmanuel Latte Lath skilfully added a second before the break.
Finn Azaz set up the second and added a third just six minutes into the second half, before Burgzorg's second put the game beyond the visitors in the 54th minute.
Jordan Clark's strike was nothing more than a consolation as Luton's misery was further compounded by Azaz's stunning curling finish with three minutes left.
If results go Middlesbrough's way, they could keep their place in the top six going into the international break, but Luton are 20th after registering their eighth loss since returning to the second tier.
Elsewhere, Cardiff City missed their chance to move clear of the relegation zone after suffering a 3-1 defeat to Blackburn Rovers, who ended a three-match losing streak on the road.
Andreas Wiemann scored early on in both halves, tapping in both from close range to give Blackburn the advantage.
David Turnbull gave Cardiff hope, turning in the rebound of his own saved penalty, but Lewis Baker's late effort wrapped up the result in the 86th minute, moving John Eustace’s side up to ninth.
Ben Gibson salvaged a point for Stoke City against Millwall, ending the visitors’ four-match winning run.
Josh Coburn had given Millwall the lead from very close range shortly before the break, netting with their first shot on target, but Stoke fought back thanks to Gibson's flicked header from a corner.
The Potters are up to 11th for now, while Millwall leapfrog West Brom into seventh.
Harris, in his second managerial stint with the club he made 374 appearances as a player, steered the Lions away from relegation last season.
However, despite Millwall sitting 11th in the Championship and six points off the play-off places, the 47-year-old has chosen to leave the club.
The Lions had been on a nine-game unbeaten run before losing 1-0 to Frank Lampard's Coventry City on Saturday, in what was the former Chelsea midfielder's first win since taking over the Sky Blues.
Harris will, however, stay in position for Wednesday's clash against league leaders Sheffield United and then away at Middlesbrough this weekend before leaving.
Millwall chairman James Berylson, said: “At the start of 2024, we found ourselves in a tough spot. Neil came in and, along with his coaching staff, galvanised the squad.
“Through action and leadership, he led Millwall on a magnificent run of form, ensuring our return to Championship football this season.
“I want to thank Neil for all his efforts since returning to the club, and we will be forever grateful to him for that.
“After discussions with Neil in recent days, he felt it was the right time to step down from the role following the Middlesbrough game and I have accepted his decision."
In a letter to fans explaining his departure, Harris wrote: “Today I am announcing that I will be leaving Millwall Football Club after Saturday’s game against Middlesbrough.
“This isn’t an easy decision, as everyone knows this club is more than a job to me, it's my club, and always will be.
“Being here always felt like home, as a player, as a captain, and as a manager. We are a family, and it's been my life for so many years. But I always said when I returned that I would leave when the time felt right, and now is that time.
“Coming back last season and all the highs that came with it will never be rivalled. It was one of the highlights of my career. We fought together as a team, as fans and as a united football club.
“We have some special characters in this team. They are dedicated and hungry to do well. With the right encouragement and support, I’m sure they can achieve great things.
“I would like to thank all the staff at the club for their loyalty and support and especially the owner, James Berylson, for welcoming me back. He's been superb to work with, and I will always be grateful for the great friendship we shared.
“We have the most passionate fans in the country, and your support has meant the world to me. We are often misunderstood, but the uniqueness of Millwall is also what makes us so special.
“I wish all of my friends at Millwall Football Club the best for the rest of the season and I will see you soon. Chopper.”
The Black Cats' four-game winning run to begin the season was ended by Plymouth Argyle last weekend, but they responded well on home soil.
Local lad Chris Rigg, aged just 17, earned Sunderland Wear-Tees bragging rights with an outrageous backheel after 24 minutes.
Middlesbrough had chances but lacked a cutting edge as Sunderland made it three clean sheets from three home league games this season.
The win lifted Regis Le Bris' men back into top spot in the early Championship standings ahead of West Brom facing Plymouth later in the day.
Elsewhere in the early kick-offs, Johannes Thorup earned his first home league win as Norwich City manager in a 4-1 victory over Watford.
The Canaries' only other win this season came on their travels at Coventry City last month, but they were good value for their latest triumph.
Callum Doyle's long-range opener was cancelled out by Ryan Andrews' strike, before Borja Sainz restored the hosts' lead just before half-time.
Marcelino Nunez added a third nine minutes into the second period and Ben Chrisene made certain of the three points late on.
QPR drew 1-1 with London rivals Millwall at Loftus Road, meanwhile, with both sides remaining in the bottom half of the table with one win apiece.
Duncan Watmore rounded off a nice team move to put Millwall ahead after 34 minutes, but Michael Frey poked home a leveller four minutes later and neither side could find a winner.
Regis Le Bris' side found themselves 2-0 down inside 17 minutes at the Swansea.com Stadium, following goals from Zan Vipotnik and Liam Cullen.
But the Black Cats got back into the match on 28 minutes through Dan Ballard, who headed home from Trai Hume's free kick to score his first league goal since December 2023.
Dan Neil restored parity with a stunning strike from distance after being picked out by Jobe Bellingham, with the Sunderland midfielder rifling the ball home off the crossbar.
Bellingham then sealed the victory two minutes later, arriving late in the box to thump Chris Rigg's cutback beyond Lawrence Vigouroux for his third goal of the season.
The result saw Sunderland move up to third in the standings, while Swansea dropped to 10th in the division after suffering their first defeat in four Championship games.
Elsewhere, Sheffield United took top spot back in the second-tier following a 2-0 victory over lowly Plymouth Argyle at Bramall Lane, piling more pressure on head coach Wayne Rooney.
Goals from Gustavo Hamer and a late Kieffer Moore penalty secured a comfortable win for the league leaders, who lead Leeds by three points. Plymouth, meanwhile, are a point from safety after their fourth straight defeat.
Sheffield Wednesday got their play-off push back on track with a 3-1 victory over Oxford United at the Kassam Stadium, which was their third win in five matches.
Greg Leigh had got the hosts ahead in the first half, before Josh Windass equalised before half-time.
Jamal Lowe netted four minutes into the second half to put the Owls in front, before Djeidi Gassama volleyed in on 61 minutes to make things more comfortable for Danny Rohl's side.
Wednesday are ninth in the table, five points below sixth, while Oxford are 20th and just one point above the relegation zone.
Millwall were beaten 1-0 away to Middlesbrough in Neil Harris' final match as manager, having announced earlier this week that he would step away from his position.
Emmanuel Latte Lath got the only goal of the game after 10 minutes to seal a result that saw Michael Carrick's side go sixth. Millwall are 13th on 25 points after 20 matches, with the search for a new head coach already underway.
Aaron Connelly had given Sunderland the lead just 10 minutes in, benefitting from a clearance to beat Lukas Jensen on the volley and claiming his first goal for the club before the players were taken off the field for half an hour due to two medical emergencies in the crowd.
Millwall were a different side when they came back out onto the pitch, with Anthony Patterson having to pull off a string of fine saves to preserve Sunderland's lead.
The hosts eventually got a deserved goal in the 93rd minute though, as Femi Azeez stabbed home Aidomo Emakhi's cross for his first Millwall goal.
It is a fourth consecutive draw for Sunderland, who sit above Sheffield United on goal difference, while Millwall stay eighth.
Elsewhere, Middlesbrough moved back into the playoff places with a thumping 6-2 victory over Oxford United.
A hat-trick from Emmanuel Latte Lath, a double from Finn Azaz and another from substitute Tommy Conway saw Boro score six goals in an away league game for the first time in 64 years.
Greg Leigh had given the hosts a surprise lead, and though Dane Scarlett halved the deficit with his second-half goal to make it 4-2, they could not mount a comeback, leaving them 18th in the table, while Middlesbrough jumped up to fifth.
Meanwhile, Luton Town eased some of the pressure on manager Rob Edwards with their 1-0 win over struggling Hull City to move out of the drop zone.
Mark McGuiness scored the only goal of the match in the 33rd minute, brilliantly volleying his maiden Hatters goal in to help Luton move up to 16th.
Hull could not find a winner, despite Joao Pedro hitting the post in the first half, and they dropped into the relegation zone as their winless run extended to eight matches.
Norwich City are on a run of seven games without a win after playing out an entertaining 2-2 draw with West Brom.
Emiliano Marcondes and an own goal from Torbjorn Heggem gave Norwich the lead after Mason Holgate's early opener, but Josh Maja's 10th goal of the campaign cancelled out their lead just before half-time to earn them a point.
Leeds moved level on points with Sunderland 24 hours earlier with victory over Watford, but Regis Le Bris' men responded well thanks to Romaine Mundle's superb winner shortly after the hour mark.
The visitors had earlier taken the lead 10 minutes into the second half through growing talent Chris Rigg's third goal of the campaign, following an error from Tahith Chong, before Elijah Adebayo swiftly levelled with a header from close range.
But Mundle's fine finish into the far corner from outside the box secured an eighth win in 11 matches for Sunderland, who have a small buffer at the summit.
Burnley join Leeds in sitting three points off the pacesetters after drawing 1-1 against Hull City at the MKM Stadium to make it eight games without defeat.
Xavier Simon opened the scoring for Hull just before half-time with a heavily deflected shot that got the better of James Trafford.
Scott Parker's visitors found an equaliser through Zian Flemming 13 minutes from time - the Dutch midfielder powerfully heading in Jaidon Anthony's back-post cross - but they wasted a big chance to take all three points as Anthony missed from close range in added time.
Elsewhere on Wednesday, Sheffield United fell to a second successive defeat without scoring as they went down 1-0 to Middlesbrough at the Riverside Stadium.
Substitute Emmanuel Latte Lath met Finn Azaz's cross in the 80th minute to head in the only goal of the game, after Jesurun Rak-Sakyi had earlier had a shot blocked on the line by Luke Ayling.
The Blades drop to fifth in the table, level on points with West Brom and Blackburn Rovers either side of them, after the pair played out a 0-0 draw.
Albion went closest to scoring in a game of minimal chances as their winless run stretched to five matches, while Blackburn dropped points at home for the first time this campaign.
The day's other game saw Romain Esse's 13th-minute strike earn 13th-place Millwall a 1-0 win over Plymouth Argyle at The Den, with the visitors dominating possession but not making it count for anything as they stay two points above the relegation zone.
